Normal Distribution

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Normal Distribution

The well known bell shaped curve. According to the Central Limit Theorem, the probability density function of a large number of independent, identically distributed random numbers will approach the normal distribution. In the fractal family of distributions, the normal distribution only exists when alpha equals 2, or the Hurst exponent equals 0.50. Thus, the normal distribution is a special case which in time series analysis is quite rare. See: Alpha, Central Limit Theorem, Fractal Distribution.

Bell Curve

A curve on a chart in which most data points cluster around the median and become less frequent the farther they fall to either side of the median. When plotted on a chart, a bell curve looks roughly like a bell.
References in periodicals archive ?
Thus, we present the calculation process of paired t-test and independent t-test in the data analysis, respectively, under the assumption that both samples come from normally distributed populations with unknown but equal variances.
The normally distributed random errors and outliers in observations also produce data jumps, whose magnitudes are examined by the model of pseudo normally distributed random errors described in the section 3.
Based on Figure 4, the histogram shows that there is a bell-shaped indicating that the error terms are normally distributed.
This means that we cannot assume that the data are normally distributed.
Under suitable conditions, this random variable is asymptotically jointly normally distributed.
Linear regression assumes that the scatter around the line is normally distributed.
Hassan (2002) found that Dow Jones Islamic Market Index [DJIMI] returns are normally distributed and the DJIMI has a remarkable market efficiency.
Note: Student's t-test was used for means comparison of normally distributed variables while Mann-Whitney U test was used for medians comparison of non-normally distributed variables.
The random parameters might be normally distributed or ln-normally distributed.
From a mathematical point of view, the essential goal of this latter step is to transform the SPI series into normally distributed series with zero mean and unitary variance.
This means based on empirical data, that the series of return is not normally distributed.